1. Longitudinal beam parameters and stability
E. Shaposhnikova, J. E. Muller
6th HL-LHC collaboration meeting, Paris
15 November 2016
Acknowledgements: P. Baudrenghien, H. Timko

2. Outline Summary Experience from present LHC operation HL-LHC
Bunch length
Stability
Longitudinal emittance blow-up and distribution
HL-LHC
Single RF operation
Double RF operation
higher harmonic
lower harmonic
Summary

3. Bunch length during physics
2012: 4.0 TeV
2015: 6.5 TeV

4. Longitudinal beam stability in LHC
Single bunch stability threshold is well defined by measurements in MDs and operation (long fills)
J. E. Muller et al.
→ Single bunch instability for multi-bunch beam
No wideband FB in LHC → we rely on Landau damping

5. Controlled emittance blow-up
Synchrotron frequency distribution inside the bunch
Phase noise
Bunch length bifurcation during emittance blow-up for 0.85 ns target length in 2015 MD
Similar observations in 2016 MDs and initial operation with reduced bunch length
→ Increased initial target bunch length during ramp in 2016 operation

6. (Un)controlled emittance blow-up
H. Timko
→ Maximum bunch length ~ 1.5 ns limited by losses (~5%) from the RF bucket
(MD ramp with target bunch length 1.2 s leading to maximum gain in BL FB)

7. Longitudinal beam parameters
Bunch-to-bunch variation (from injectors) leads to different synchrotron frequency shifts and therefore final emittance blow-up (denser bunches are blown up less)
→ Bunch-to-bunch length variation after controlled emittance blow-up (BUP)
Beam-to-beam and fill-to-fill variation (also due to action of bunch length feedback)
→ Variation in instability threshold
Synchrotron frequency distribution after BUP (PD Schottky spectrum)

8. Longitudinal beam stability in LHC
Preliminary results of MD on (T. Mastoridis, J. E. Muller, E. Shaposhnikova, H. Timko et al.)
Beam1
V=7.5 TeV, nominal intensity
Beam1:
Target bunch length 1.1 ns
(1.05 ns obtained)
→ All bunches above single bunch instability threshold
→ No coupled-bunch modes were observed, but phase oscillations with amplitude increasing along the beam
Beam1: flat top

9. Longitudinal beam stability in LHC
Phase oscillations on flat bottom and during ramp for nominal beam with 1.2 ns target bunch length (blow-up and after arrival to flat top)
Beam1:
flat bottom
average/(SPS batch)
during ramp and
flat top

10. HL-LHC

11. Double RF operation
Full detuning scheme will be used in operation for high intensity beams
(P. Baudrenghien et al.)
leading to bunch displacements
→ Only bunch-shortening operation mode is really feasible in a double RF system
V2/V1=2

12. Longitudinal beam stability in HL-LHC 400 MHz & (400 MHz + 800 MHz) RF
E=7 TeV, V400 = 16 MV, V800 = 4 MV
ImZ/n ~ 0.11 Ohm (N. Biancacci et al.)
→ 1.0 ns bunches are unstable
→ Voltage of MHz would be sufficient for stability of bunches > 0.85 ns
(as now)
10% spread in bunch length
Controlled longitudinal BUP, if done too close to instability threshold, may excite dipole motion
SR leads to bunch shrinkage
→ 1.2 ns nominal average bunch length in a single RF system
Cavity design: T. Roggen & Y. Shashkov

13. Longitudinal instability for HL-LHC intensity
Bunch length during ramp
Bunch length on LHC flat top
RF MD on , V=12 MV, P. Baudrenghien, J. Muller, H. Timko, E. S.

14. Longitudinal beam stability in HL-LHC: 200 MHz & (200 MHz + 400 MHz) RF
V200=6 MV, V400=3 MV
Reduction of e-cloud, beam-induced heating, pile-up density…
→ Bunches with 1.9 ns length are at the limit of stability in a single RF and with 1.4 ns in a double RF (BSM)
→ Operation (assuming 10% spread
and uncertainty in BUP):
τav > 1.55 ns in 2RF → 1.7 ns
τav > 2.1 ns in 1RF → 2.3 ns
Cavity design: R. Calaga

15. Longitudinal beam parameters in 1 & 2 RF systems for stable TeV with 2.2x1011 ppb & minimum (average) bunch length
RF system V1
[MV] V2
Bunch length (4σ)
[ns]
Emittance
(2σ)
[eVs]
dE/E
[10-4]
400 MHz
16.0
0.0
1.2
3.0
2.36
400 & 800 MHz (BSM)
8.0
0.85
2.1
2.32
4.0
1.0
2.5
 2.34
200 MHz
6.0
2.3
4.85
1.97
200 & 400 MHz (BSM)
1.7
3.6
2.0
Based on single-bunch stability threshold (loss of Landau damping) for beam
with 10% spread in bunch length and with additional 10% margin (shrinkage due to SR damping and uncertainty in emittance blow-up)

16. Bunch distribution in single RF system
Binomial line density distribution λ(t) = λ0 (1 – 4 t2/τ2) fits well the present LHC bunches (single RF) on flat bottom and at the beginning of flat top (after controlled emittance blow-up with band-limited noise during ramp)
Real bunch tails are more populated (also visible from the PD Schottky)
Profiles become Gaussian after a few hours due to IBS and SR

17. Bunch distribution in double RF system
Example of double RF system with V2/V1=0.5 in BSM
Band-limited noise applied to the bunch centre flattens the profile
Tested in BLonD simulations (H. Timko)
bunch
profiles
bunch
spectra
particle
distribution
functions

18. Summary
In the 400 MHz RF system longitudinal stability of bunches with nominal HL-LHC length of 1.08 ns is at the limit. Margins are required due to bunch-to-bunch and fill-to-fill variations together with shrinkage due to synchrotron radiation.
Stability is recovered for 1.2~ns long bunches in single RF or in double for 1.0 ns with 4 MV at 800 MHz. Possible uncertainties due to increased HL-LHC impedance and coupled-bunch instabilities.
Beam lifetime is reduced for bunch length more than 1.5 ns (in the 400 MHz RF): → narrow operational window ( ) ns
New operation regime with long (> 1.7 ns) bunches in 200 MHz (+ 400 MHz) RF system has many advantages (e-cloud…)
Double RF system should make controlled emittance blow-up during ramp more reliable

19. SPARE SLIDES

20. Capture 200 MHz RF system: needs from the SPS

21. Impedance reduction of vacuum flanges: 72 bunches 2RF systems (1 MV @ 800 MHz)
With 1.5 MV at 800 MHz
the threshold increase
is already sufficient,
but margin is still small
24 b
2 RF
72 b
1.5 MHz
1 MHz
24 b
1 RF
72 b
BLonD simulations
A. Lasheen & J. Repond

22. Possible uncertainties
Available voltage (very high RF power, main power couplers, LLRF: pulsing mode of operation)
SPS impedance model
still some impedance missing (synchrotron frequency shift)…
Simulations
Done for 1 batch of 72 bunches on the flat top
Stability during ramp (work in progress)
Don’t include longitudinal damper, phase loop, phase error,…

23. Nominal injected emittance & BUP: RF power for longer cycle and Q22

24. Summary - SPS
From the RF point of view we should be able to obtain HL-LHC parameters after the 200 MHz RF upgrade and LIU baseline longitudinal impedance reduction
We rely on simulations and it is difficult to take into account all possible uncertainties
Extra margins can come from
bunch rotation on the SPS flat top
5% longer bunches at injection into the LHC
200 MHz RF system in the LHC
Further longitudinal emittance increase in the SPS is limited by beam loading in the 200 MHz RF during ramp